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Turns, Dark Energy, Dark Matter, and Spooky Action at a Distance

and now for something completely different...

This is the key identity:

We know that, since space is isotropic, the identity must hold true both locally and globally. This is not an issue in flat Euclidean 3-space. However, once we include time into the model and are confronted with relativity, some issues arise. How does the identity remain true both locally and globally?

The answer appears to be that , and are not only dimensionless quantities as we tend to think they are, but they can also be combined in order to make an actual quantity (or scalar, or magnitude, or a measurable entity, or however you wish to say it.)

Because this is the case, the addition of time into the coordinate system can be accomplished by understanding that when this is done (when time is introduced), the coordinate system must wrap back on itself. This is an abstract solution, but it illustrates the problem with having this new identity hold true in the global and local domain. By this I mean that the equation holds true for both sets of points, those that are adjacent and those that are not.

Once you grasp the significance of this reality it becomes clear that the dark energy doesn't exist in the "model" and that's why we don't see it. Once energy becomes oriented such that it is perpendicular to the "model," it disappears because its amplitude goes to zero while its wavelength goes to infinity. It's a geometric artifact created by the way we choose to make the "model" mathematically or, more specifically, geometrically.

An alternative model uses time, length, and direction as the three dimensions. We have coined the term "synchronous geometry" to differentiate this model from the standard model. In this model things flip symmetrically with the way they are represented in the standard model. In synchronous geometry the length triplet that is used to identify a point or event is replaced with a direction triplet. The vector quantity that is present in the standard model (direction) becomes the scalar quantity in the synchronous model.

Following along, the scalar value (length) in the standard model becomes the vector quantity. In the standard model the direction has no magnitude or scalar quantity or length. In the synchronous geometry, where things are swapped, the length has no direction (think of it as the radius of a sphere) since direction is the scalar quantity in this version of spacetime (or more accurately, Euclidean 3-space).

Because this can be done, it becomes clear (or murky) that there should be an additional effect on the phenomenon that we call frame-dragging, which is more clearly another artifact of the way we are choosing to do the math. Rather than try and explain the math (since I don't have the algebra skills to write the expressions that would be necessary to get the point across), I can suggest another thought experiment.

The rings of Saturn are orbiting the gas giant and are frame-dragging spacetime around with them. If we were to look closely at the interface between the plane in which the frame-dragging is represented mathematically and the adjacent spacetime, we should see one of two things: either the spacetime that the gas giant occupies adjacent to this plane interacts identically with the frame that is being dragged, or, the two sides interact differently due the effect on spacetime caused by the Sun's gravity. In other words, the advancing and retreating sides of the frame, relative the Sun's field, will produce different effects. Doesn't this mean that the spacetime itself is rotating in the frame? I think it does mean that, except that I don't have the math skills to show it one way or the other.

In any event, the dark matter question is another effect caused by the same issue with how we do the math. It isn't a trivial thing to understand this or to explain it to someone. It is impossible to explain it to anyone who doesn't understand the identity above, or what it means. My best description of it is to say that directions or angles can be used to construct a coordinate system in a symmetrically identical manner as what is done in the Cartesian system.

Having briefly looked at how we model quanta mathematically, it sure looks like the same question arises there as regards to how we are using the standard model of spacetime. In the synchronous model it is almost trivial to show how energy states transition at the rates at which they occur. There isn't really a step-function, but rather a hyperbolic function that goes to zero. Also, once direction is viewed as a quantity it becomes clear (or murky) that direction has no sign associated with it, which very likely explains spooky action at a distance. We have time and distance which each have signs associated with them and direction which does not have a sign associated with it. These are the three quantities that exist in synchronous geometry.

When distance (ength) and ime are combined in spacetime the result is bounded by and :

When direction (urns) and ime are combined in spacetime the result is bounded by zero and infinity:

Note that the sign is actually associated with length rather than direction. This has an effect when spacetime is curved.

I assume "pooky" action was just a typo and you created a duplicate thread. I've deleted the other thread. In the future, rather than creating a duplicate thread, please ask a moderator to fix the typo in the title.

You linked to tusenfem's own post in a previous thread and it doesn't even directly answer the question. And we are not going to go poking around in a 263 post thread of your's for the answer. Nor are you going to get to plug your website.

You will directly and completely answer the question right here in your very next post, or you will be infracted.

And if this is just a rehash of one of your many previous threads, you will be suspended.

And we don't respond well to commenting on moderation in the thread. Read the forum rules about ways you can use when you have a problem with a certain post. This is not one of those ways.

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I guess you would have to explain first what , and are, and then how you obtain such a convoluted equation.

Since this post is not in your moderator voice, I will respond to it directly. Either you are feigning ignorance regarding how the convoluted formula was obtained, or you actually forgot about it. In either case it is appropriate for me to try and jog your memory.

Why can't there be an honest discussion of the physics, without recriminations? This area of inquiry will exist regardless of how any us behaves.

Followed by no ATM idea: steveupson!
A "key identity" that has nothing to do with Dark Energy, Dark Matter or Spooky Action at a Distance. It has nothing to so with space in this universe other than your unsupported speculations after it. The thread you link to is a math thread with no physics.
As soon as you wrote "Euclidean 3-space" in this thread you falsified your speculations. The universe is not Euclidean.

...we call frame-dragging, which is more clearly another artifact of the way we are choosing to do the math.

Frame dragging is a scientific prediction from GR, not an "artifact ". The latter "I don't have the algebra skills", "I don't have the math skills" comments make that assertion unfounded.
The Saturn rings thought experiment shows that you need to learn the physics. Frame dragging is so small effect that we had to put very precise instruments in orbit to measure it in Gravity Probe B. Even then it took a few years of analysis before GR's prediction was confirmed.

In any event, the dark matter question is another effect caused by the same issue with how we do the math.

Dark matter is several sets of different observations, not math - observational evidence for dark matter.
And again - you have stated you do not have the skills to know whether there is any issue with how we do the math. An obscure, irrelevant identity has nothing to do with the math in the observations, the math in particle physics (the best explanation) or the math in modified physics (MOND, etc.).

Followed by a series of vague, unsupported assertions. There is no "synchronous model" in this thread, etc.
There is no energy state "step-function" in quantum mechanics. That energy transitions are quantized is empirical evidence. QM started with Planck's law where Planck found that measured black body radiation could be explained by photon energy being quantized. Einstein showed that this also explained the photoelectric effect in 1905. Elements emit spectral lines that come in series described by the Rydberg formula in 1888. This lead plus the discovery that atoms are electrons "orbiting" a nucleus to the 1913 Bohr model where the energy of the electrons set as quantized. A couple of decades later we get the Schrodinger equation where energy being quantized is a mathematical consequence of a particle being bound.

The evidence for dark energy is indirect but comes from three independent sources:

Distance measurements and their relation to redshift, which suggest the universe has expanded more in the last half of its life.[22]

The theoretical need for a type of additional energy that is not matter or dark matter to form the observationally flat universe (absence of any detectable global curvature).

It can be inferred from measures of large scale wave-patterns of mass density in the universe.

JP: Indirect evidence is not seeing that dark energy exists!

James Putnam

ATM is not a collaborative effort. It is entirely steveupson's responsibility to answer questions and concerns in this thread. If you want to give him help, drop him a PM, but do not present any arguments in his support or respond to questions addressed to him.

Dark matter is several sets of different observations, not math - observational evidence for dark matter.
And again - you have stated you do not have the skills to know whether there is any issue with how we do the math. An obscure, irrelevant identity has nothing to do with the math in the observations, the math in particle physics (the best explanation) or the math in modified physics (MOND, etc.).

Do you have some authoritative source for this claim, or is it more hand waiving? Maybe we can come to some
sort of understanding if we drill down on this idea.

There are 141 authorities sources cited in the article. Or you could read some physics textbooks. Or you could read the literature: The SAO/NASA Astrophysics Data System (only 74,787 abstracts for 'dark matter' )

There are observations that

The dynamics of galaxies in clusters needs more matter than is visible.

The velocities of stars in galaxies needs more matter than is visible.

When 2 galaxy clusters collide there are two kinds of matter - one the emits light and interacts electromagnetically and another that is dark and does not interact electromagnetically.

The properties of the CMB cannot be matched by models unless we add dark matter.

I must not have made it clear in the OP that my claims are mathematical. More specifically, they have to do with geometry and how much we rely on it to describe physical phenomena using the language of mathematics.

The specific formula, although obscure, does seem to me to throw a wrench into our understanding of how Euclidean 3-space transforms into spacetime when we add time to the mix.

The math isn't simple. The comments regarding the math are either that it is uninteresting high school trig or that it isn't explained well enough for anyone to follow it.

I want to apologize to the other members for losing control. I'm frustrated and I was wrong about the way that I treated tusenfem upthread. After some reflection I realize that they were probably not being disingenuous after all, and I shouldn't have interpreted it that way.

The premise isn't that complicated, really. Only the math is hard. The premise is that scientists always consider all known mathematical relationships when formulating their mathematical representations of nature. The key identity is a new unknown relationship that has not been accounted for in any of the models. It really is that simple.

The new relationship or identity is simply the slope of the tangent to a circle. The thing that makes it special is that it is new. The thing that makes it new is that nobody needed to know this relationship before. There's well-known work-around for solving these types of problems. The work-around is parallel transport. This new relationship is not expressed when parallel transport is implemented.

Draw a small circle on a unit sphere. As you traverse the circumference of the circle, note the slope of the tangent at each point. The key function does exactly this.

This relationship is fundamental in the same way that the sine and cosine are fundamental functions. It is a smooth function that approaches a sine curve when the radius of the small circle approaches zero, or , and that approaches a hyperbola when the radius of the small circle becomes a great circle .

Angle is the spherical angle between the tangent point and the north pole of the sphere. Angle is the tangent angle, relative to a line of longitude.

The premise isn't that complicated, really. Only the math is hard. The premise is that scientists always consider all known mathematical relationships when formulating their mathematical representations of nature. The key identity is a new unknown relationship that has not been accounted for in any of the models. It really is that simple.

The problem is that you have not shown any of your claims are valid. You say this is a very important identity that explains things like frame dragging, dark energy and dark matter observations in a different and presumably better way. But then you say that you can't do the maths, or that the maths is too hard for anyone else to understand, and resort to a series of deeply unconvincing 'explanations' that apparently are totally convincing if I could just understand your idea as well as you do.

If your ideas are that powerful then show here, in detail and with all your working, the evidence for your claims.
1) Derive the Schiff precession rate for the Gravity Probe B set-up and show that it is consistent with the published measurements (http://einstein.stanford.edu/highlights/status1.html)
2) Predict the precession rate you'd expect to see around the SMBH at the galactic core
3) Derive the expected rotation curves for our galaxy and show that it is consistent with measurements
4) Use the same model as above to account for Dragonfly 44
5) Derive the distance luminosity relationship for type Ia supernovae and show that this is consistent with observations
6) Show how your ideas lead to the characteristic structure in the power spectrum of the CMB (the BAO)
7) Show how your ideas account for the observed elemental abundances in the universe and show that this is consistent with stellar nucleosynthesis.

If you cannot show quantitative predictions on at least some of the above textbook cases then you have absolutely no grounds for the claims you are making. If this is too much I suggest you pick your claim for which you believe your evidence and theory to be strongest and present that in detail. As things stand your ideas fall into the category of non-falsifiable (due to a lack of any detail) and non-predictive (as there seems to be no formal logical structure leading to your claims).

If all you are going to do is make claims and insist that they are obviously true provided we understand things as well as you then I'm not going to engage here. The onus on anyone with a new idea is to show that it is worth other people putting in the time to understand it - and so far you fall far short of that for me.

The problem is that you have not shown any of your claims are valid. You say this is a very important identity that explains things like frame dragging, dark energy and dark matter observations in a different and presumably better way. But then you say that you can't do the maths, or that the maths is too hard for anyone else to understand, and resort to a series of deeply unconvincing 'explanations' that apparently are totally convincing if I could just understand your idea as well as you do.

Perhaps you can tell me how much you do understand of the math. That way I could better explain the parts that you don't understand.

Perhaps you can tell me how much you do understand of the math. That way I could better explain the parts that you don't understand.

I understand trigonometry just fine. What I don't understand and what you have not presented here is how either your geometric construct or your identity leads to the claims you have made. I have asked you to present the detailed analysis that allows you to make these sweeping claims - can you please answer my questions?

Perfect. The key identity spans the void that exists between the circular functions and the conic functions.

What is happening is that three separate angles in three separate planes have a geometric relationship to one another that can be expressed in a two-dimensional graph, similar to a sine curve or a hyperbolic curve. As a matter of fact, at one limit the curve is a sine curve and at the other limit the curve is a hyperbola.

Perfect. The key identity spans the void that exists between the circular functions and the conic functions.

What is happening is that three separate angles in three separate planes have a geometric relationship to one another that can be expressed in a two-dimensional graph, similar to a sine curve or a hyperbolic curve. As a matter of fact, at one limit the curve is a sine curve and at the other limit the curve is a hyperbola.

And this leads to your claims about frame dragging, dark energy and dark matter via the quantitative predictions and detailed model you are about to present here?